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Moyal Deformations of Gravity via SU(∞) Gauge Theories, Branes and Topological Chern-Simons Matrix Models

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Abstract

Moyal noncommutative star-product deformations of higher-dimensional gravitational Einstein-Hilbert actions via lower-dimensional SU(∞), W ∞ gauge theories are constructed explicitly based on the holographic reduction principle. New reparametrization invariant p-brane actions and their Moyal star product deformations follows. It is conjectured that topological Chern-Simons brane actions associated with higher-dimensional “knots” have a one-to-one correspondence with topological Chern-Simons Matrix models in the large N limit. The corresponding large N limit of Topological BF Matrix models leads to Kalb-Ramond couplings of antisymmetric-tensor fields to p-branes. The former Chern-Simons branes display higher-spin W ∞ symmetries which are very relevant in the study of W ∞ Gravity, the Quantum Hall effect and its higher-dimensional generalizations. We conclude by arguing why this interplay between condensed matter models, higher-dimensional extensions of the Quantum Hall effect, Chern-Simons Matrix models and Gravity needs to be investigated further within the framework of W ∞ Gauge theories.

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  1. Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, Georgia, 30314, USA

    Carlos Castro

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Castro, C. Moyal Deformations of Gravity via SU(∞) Gauge Theories, Branes and Topological Chern-Simons Matrix Models. General Relativity and Gravitation 36, 2605–2634 (2004). https://doi.org/10.1023/B:GERG.0000048962.79491.a3

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